Quantum entanglement underlies many fundamental quantum tasks [1]}, [2]} and is often considered synonymous with quantum correlations in early studies, although it is now recognized that the notion of quantum correlations is much broader in scope, and that entanglement is a particular, though most important, type of quantum correlation, i.e., quantum entanglement can be identified as nonlocal quantum correlations [3]}. The study of entanglement explicitly dates back to the seminal work of Einstein, Podolsky and Rosen [4]}, and of Schrödinger [5]}, [6]} as early as the 1930s. Today, entanglement is considered a key resource of quantum information and is often linked to quantum non-locality [7]}, [8]}. In 2002, after studying the correlation between the device and the system during a measurement, Ollivier and Zurek [9]} realized that separable states, as defined by Werner [3]}, can still have some correlation in the sense that they can be perturbed by local measurements. This novel measure of quantum correlations beyond entanglement is called quantum discord [11]}, [12]}, [13]}. They found that entanglement is not the only quantum correlation that has no classical counterpart. Other types of quantum correlations, such as quantum discord, may also be responsible for speeding up some quantum algorithms while entanglement may disappear or be negligible [14]}. Since the first statements of this concept, many research efforts have been devoted to understanding the mathematical properties and physical meanings of discord and similar quantities. Comprehensive review of the properties of quantum discord is available in [15]} and the Refs.[16]}, [17]} provide recent insights into this field. Indeed, the investigation of quantum discord presents many challenges and open questions. A major difficulty with discord-like quantities is that they are difficult to calculate or to analyze. Formally, quantum discord is defined as the difference between the quantum mutual information (quantifying the total correlation) and the maximum amount of mutual information accessible to a quantum measurement (quantifying the classical correlation). To quantify the locally accessible (classical) correlations, this quantification involves an optimization over all possible local measurements. This measure is chosen to maximize the classical correlations. Due to the complexity of the optimization process, the computation of the quantum discord and its variants (such as the geometric discord) is not an easy task and the analytical results are only known for some restricted families of states. To overcome this problem, several other versions of discord have also been proposed, including linear quantum discord [18]}, local quantum uncertainty [19]}, [20]}, and local quantum Fisher information [21]}. Most of these quantum correlation quantifiers for pure quantum states can be coincidental and can sometimes exhibit similar behavior for mixed states.
